Question: Simplify; express your answer in exponential form. Assume $x\neq 0, k\neq 0$. $\dfrac{{xk}}{{(x^{5}k^{3})^{2}}}$
To start, try simplifying the numerator and the denominator independently. In the numerator, we can use the distributive property of exponents. ${xk = xk}$ On the left, we have ${x}$ to the exponent ${1}$ . Now ${1 \times 1 = 1}$ , so ${x = x}$ Apply the ideas above to simplify the equation. $\dfrac{{xk}}{{(x^{5}k^{3})^{2}}} = \dfrac{{xk}}{{x^{10}k^{6}}}$ Break up the equation by variable and simplify. $\dfrac{{xk}}{{x^{10}k^{6}}} = \dfrac{{x}}{{x^{10}}} \cdot \dfrac{{k}}{{k^{6}}} = x^{{1} - {10}} \cdot k^{{1} - {6}} = x^{-9}k^{-5}$